The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
Parallel magnetic resonance imaging (pMRI) employs the following image reconstruction methods:
1. Simultaneous acquisition of spatial harmonics (SMASH)
2. Variable density-AUTO-SMASH (VD-AUTO-SMASH)
3. Generalized auto-calibrating partially parallel acquisitions (GRAPPA)
4. Multi-column multi-line GRAPPA: 2D-GRAPPA
5. Method and device for magnetic resonance imaging on the basis of a partially parallel acquisition (PPA).
SMASH is one of the methods for reconstructing images in k-space. SMASH acquires image information by performing sub-sampling in the ky-direction in k-space in order to reduce image acquisition time.
In this case, image information that is acquired from each channel may be represented by Equation 1:S(kx,ky)=∫∫dxdyCj(x,y)ρ(x,y)e-ikxx-ikyy  Equation 1
In Equation 1, Cj(x,y) is the sensitivity profile of a j-th channel, and ρ(x,y) is overall image information to be reconstructed. Assuming that Ccomp is the sum of values obtained by multiplying the sensitivity profiles of respective channel images by a specific constant, a value nj that allows Ccomp to become spatial harmonics may be acquired, as indicated in Equation 2 (see FIG. 1), and the constant by which the sensitivity profiles of respective channels should be multiplied in order to form Ccomp is estimated using the sensitivity profiles of the respective channels images.
                                          C            comp                    ⁡                      (                          x              ,              y                        )                          =                                            ∑              j                                                                    ⁢                                                  ⁢                                          n                j                            ⁢                                                C                  j                                ⁡                                  (                                      x                    ,                    y                                    )                                                              =                      exp            ⁡                          (                              im                ⁢                                                                  ⁢                Δ                ⁢                                                                  ⁢                                  k                  y                                ⁢                y                            )                                                          Equation        ⁢                                  ⁢        2            
When the constant that allows spatial harmonics to be formed is obtained and then multiplied by the channel images, information on locations adjusted by +m or −m in the ky-direction may be acquired, as indicated by Equation 3:
                                                                        S                ⁡                                  (                                                            k                      x                                        ,                                                                  k                        y                                            +                      m                                                        )                                            =                            ⁢                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                                  ⁢                                                                  C                        comp                                            ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          ρ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          exp                                                                                                    -                            ⅈ                                                    ⁢                                                                                                          ⁢                                                      k                            x                                                    ⁢                          x                                                -                                                  ⅈ                          ⁢                                                                                                          ⁢                                                      k                            y                                                    ⁢                          y                                                                                                                                                                                            =                            ⁢                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                                  ⁢                                          ρ                      ⁡                                              (                                                  x                          ,                          y                                                )                                                              ⁢                                          exp                                                                                                    -                            ⅈ                                                    ⁢                                                                                                          ⁢                                                      k                            x                                                    ⁢                          x                                                -                                                                              ⅈ                            (                                                                                                                  ⁢                                                                                          k                                y                                                            +                                                              m                                ⁢                                                                                                                                  ⁢                                Δ                                ⁢                                                                                                                                  ⁢                                                                  k                                  y                                                                                                                      )                                                    ⁢                          y                                                                                                                                                                            Equation        ⁢                                  ⁢        3            
Unacquired information is estimated with value nj acquired using the sensitivity profiles, as described above, thereby reconstructing the overall image information.
While SMASH is the first proposed algorithm for generating harmonics by using individual sensitivity profiles in k-space and then reconstructing an image as described above, it has disadvantage that it requires sensitivity profiles to reconstruct an image and cannot compensate for image distortion attributable to interference between channels (see Sodickson, D. K. & Manning, W. J. 1997. Simultaneous Acquisition of Spatial Harmonics (SMASH): Fast Imaging Radiofrequency Coil Arrays. Magnetic Resonance in Medicine, 38(4), 591-603).
VD-AUTO-SMASH is an improvement on SMASH. In VD-AUTO-SMASH, the process of acquiring a constant used for image reconstruction by using sensitivity profiles in SMASH is replaced with the process of acquiring auto-calibrating signal (ACS) information and estimating a constant based on data. Although VD-AUTO-SMASH takes a longer image acquisition time than SMASH for acquiring a plurality of pieces of ACS information, a constant used to generate harmonics can be estimated with higher accuracy.
VD-AUTO-SMASH is an improvement on SMASH and AUTO-SMASH. Unlike SMASH, AUTO-SMASH and later methods acquire a coil-weighting factor through the process of acquiring ACS information and then fitting the ACS information to sub-sampled information, as in the second process of FIG. 2. The image information of an unacquired location is acquired using the constant value acquired by the fitting process. In this case, if m is the distance in the ky-direction between the image information of an acquired part and image information to be acquired, that is, unacquired image information, the image information of an acquired part and the image information of the unacquired image information have a relationship formed via the coil-weighting factor and the sensitivity profile, as expressed by Equation 4:
                                                                                          S                  ACS                                ⁡                                  (                                                            k                      x                                        ,                                                                  k                        y                                            -                                              m                        ⁢                                                                                                  ⁢                        Δ                        ⁢                                                                                                  ⁢                                                  k                          y                                                                                                      )                                            =                                                ∑                  j                                                                                        ⁢                                                                  ⁢                                                      n                    j                    m                                    ⁢                                                            S                      j                                        ⁡                                          (                                                                        k                          x                                                ,                                                  k                          y                                                                    )                                                                                                                                              =                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                  ∑                        j                                                                                                                      ⁢                                                                                          ⁢                                                                        n                          j                          m                                                ⁢                                                                              C                            j                                                    ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                  ρ                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                  ⅇ                                                                                                                    -                                ⅈ                                                            ⁢                                                                                                                          ⁢                                                              k                                x                                                            ⁢                              x                                                        -                                                          ⅈ                              ⁢                                                                                                                          ⁢                                                              k                                y                                                            ⁢                              y                                                                                                                                                                                                                                                  =                              ∫                                  ∫                                                            ⅆ                      x                                        ⁢                                          ⅆ                      y                                        ⁢                                                                  ∑                        j                                                                                                                      ⁢                                                                                          ⁢                                                                                                    C                            comp                                                    ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                  ρ                          ⁡                                                      (                                                          x                              ,                              y                                                        )                                                                          ⁢                                                  ⅇ                                                                                                                    -                                ⅈ                                                            ⁢                                                                                                                          ⁢                                                              k                                x                                                            ⁢                              x                                                        -                                                          ⅈ                              ⁢                                                                                                                          ⁢                                                              k                                y                                                            ⁢                              y                                                                                                                                                                                                                                  Equation        ⁢                                  ⁢        4            
Value njm indicating the relationship between the ACS information and the acquired signal is obtained from Equation 4, and then an image is reconstructed using value njm. Since VD-AUTO-SMASH uses a plurality of pieces of ACS information, the constant njm for each channel j and value m is acquired by the weighted sum of the plurality of constants acquired by the plurality of pieces of ACS information.
VD-AUTO-SMASH has the advantage of performing the process of acquiring sensitivity profiles based on data by introducing the concept of ACS information, and also has a robustness to noise because it uses a plurality of pieces of ACS information. However, VD-AUTO-SMASH is susceptible to image distortion because it lacks a compensation against image distortion attributable to phase distortion between channels (see Heidemann, R. M., Griswold, M. A., Haase, A. & Jakob, P. M., 2001. VD-AUTO-SMASH Imaging. Magnetic Resonance in Medicine 45(6), 1066-1074).
GRAPPA acquires part of information in the ky-direction in k-space in order to reduce image acquisition time, as in SMASH or VD-AUTO-SMASH method. However, GRAPPA acquires additional information called ACS information, as in VD-AUTO-SMASH method, and then estimates the relationship between the ACS information and acquired line information. Thereafter, information on unacquired lines is estimated along the ky-direction by using the estimated relationship, thereby reconstructing the image (see FIG. 3).
In this case, GRAPPA can improve the quality of image by using the ACS information, as in VD-AUTO-SMASH. GRAPPA has a feature that images of respective channels are separately reconstructed. As a result, the performance of image reconstruction is improved, and image distortion attributable to phase distortion between channels can be eliminated when the images of respective channels are combined together by using a square root of sum of squares (SoS) reconstruction method.
However, GRAPPA requires a relatively long image reconstruction time when the number of channels is large since individual channel images are separately constructed, and bears disadvantage due to the inability to acquire the phase information of a final image when an image is reconstructed using the SoS method (see Griswold, M. A., Jakob, P. M., Heidemann, R. M., Nittka, M., Jellus, V., Wang, J., et al., 2002. Generalized Auto-calibrating Partially Parallel Acquisitions GRAPPA. Magnetic Resonance in Medicine, 47(6),1202-1210).
Multi-Column Multi-Line GRAPPA is an improvement on the above-described GRAPPA, and is referred to as “2D-GRAPPA.” Existing GRAPPA uses only information in the ky-direction to reconstruct a missing line information. In contrast, 2D-GRAPPA additionally uses information in the kx-direction, as illustrated in FIG. 4, thereby improving the performance of image reconstruction. It is generally referred to as “2D-GRAPPA” because of its feature for reconstructing an image by using both information in the kx-direction and information in the ky-direction in k-space.
However, 2D-GRAPPA also requires separate reconstructions of images acquired for respective channels, like existing GRAPPA, inheriting the inability to acquire the phase information of a final image when the SoS method is used in combining the pieces of information of the respective channels (see Wang, Z., Wang, J. & Detre, J. A., 2005. Improved Data Reconstruction Method for GRAPPA. Magnetic Resonance in Medicine, 54(3), 738-742).
The “method and device for magnetic resonance imaging on the basis of a partially parallel acquisition” is a technology that is disclosed by U.S. Patent Application Publication No. 2009/0134870 A1. The image reconstruction process of the technology will now be briefly described. First, low-frequency images are generated by using low-frequency signals fully sampled from a plurality of pieces of image information acquired from respective channels. The low-frequency images of the respective channels are combined into a single sheet of combined image, the single combined image is subjected to inverse Fourier transform, and then image reconstruction is performed, as in GRAPPA. Using this process, the US patent application has the advantage of reducing image reconstruction time. Furthermore, the method can acquire both the magnitude and phase information of an image because a single image is reconstructed.
However, the performance according to the US patent application is variable depending on the method of combining individual channel images, and requires the process of acquiring or estimating a sensitivity map because it is essential to such method as an Adaptive Combine (see Vladimir Jellus, 2009. Method and Device for Magnetic Resonance Imaging on the basis of a Partially Parallel Acquisition (PPA), US Patent Application Publication No. 2009/0134870 A1).